CDKB Pressure Vessel Design Case Study

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Pressure Vessel Design Case Study

This case study considers the design of a cylindrical storage vessel typical of those used in chemical and process

industries to store liquids. Corrosion resistance, strength and ease of fabrication make composite materials

particularly attractive for this sort of application. The installed cost of a GRP vessel compares favourably with

that of more tradit ional materials, such as stainless steel and lined carbon steel vessels. The majority of such

vessels have diameters in the range 1 to 10 m, with wall thicknesses of between 5 and 50 mm.

In many respects, the process of designing a composite vessel is the same as that facing the designer of metal

vessels. The design must take into account the design stress resulting from the pressure and size of the vessel in

question. However, the composite designer is faced with the additional task ofdesigningthe material to be

used. In so doing, they will generally take the opportunity to use a variety of differing layers within the laminate

construction in order to achieve the most economical and desirable combination of properties.

The design methodology used in this case study is that developed in BS4994.This requires that the design

process is considered in three stages, assessment of allowable strain, calculation of the applied unit loads and

the selection of an appropriate laminate configuration.

Case Study Parameters

The vessel considered in this case study is a cylindrical vessel, internal diameter 1.75 m with an effective

pressure of 2 bar (0.2 MPa). The operating temperature for the vessel is 40C. In service, the vessel contents

level will primarily be static, although on occasion, the vessel will be emptied and refilled. The case study will

follow the design process, using the BS4994 methodology, to develop a suitable laminate configuration.

Allowable Design Strain

BS4994 determines an allowable design strain through the use of a number of part factors, which account for the

effects of loading, environment and manufacturing conditions on the long-term chemical and mechanical behaviour

of the GRP laminates.

These part factors are defined as follows:

k1 method of manufacture (range 1.6 to 3.0)

k2 long term behaviour (range 1.2 to 2.0)

k3 temperature (range 1.0 to 1.2)

k4 cyclic loading (range 1.1 to 1.4)

k5 curing procedure (range 1.1 to 1.5)

The product of these factors, and a further safety factor of 3.0 results in an overall design factor, K, which is

used to evaluate the allowable design strain, eL.

For the case considered here, these part factors are evaluated as follows:

For hand lay-up, part factor k1 = 1.6

For long term behaviour, part factor k2 = 2.0

For temperature, assuming operation at 40C, and use of a resin system with a heat distortion

temperature of 80C or higher, part factor k3 = 1.0

For cyclic stressing, assuming occasional filling and emptying, part factor k4 = 1.1

For curing procedure, assuming post cure at elevated temperature, part factor k5 = 1.1

Therefore, as

The "load limited" allowable limit loading uL is given by

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where u is the ultimate tensile unit strength (UTUS is in N/mm per kg/m2

) of the material, and K is the design

factor calculated above.

chopped strand mat (CSM) the UTuS is 200 N/mm/(kg/m2), thus uL = 17.2 N/mm/(kg/m

2)

woven rovings (WR) the UTuS is 300 N/mm/(kg/m2), thus uL = 25.8 N/mm/(kg/m

2)

The load limitedallowable strain is given by

where uand Kare as previously defined andXis the laminate extensibility.

ForCSM, the extensibility is 12 700 N/mm/(kg/m2), giving eL = 0.14%

ForWR, the extensibility is 16 200 N/mm/(kg/m2), giving eL = 0.16%

There is a further overriding upper limit to the design strain of the lesser of 0.2% or 0.1 x er(where eris the

fracture strain of unreinforced resin in a simple tensile test.

Assuming a resin strain to failure of 3%, then, in this case, the design remains load limitedand the design unit

loading ux = uL, i.e. 17.2 N/mm/(kg/m2) and 25.8 N/mm/(kg/m2) forCSMand WRrespectively.

Applied Loads

The applied loading on the vessel is then calculated using conventional analysis techniques. In this case,

assuming no significant axial loading, the vessel wall circumferential unit stress is given by:

where Pis the pressure, D is the vessel diameter and t is the vessel wall thickness.

Laminate Construction

At this point, it is possible to design the laminate construction.

The total quantity of reinforcement, in this first case for a vessel constructed simply from multiple CSMlayers, is

simply determined by:

where wxis the weight of a single layer and nx is the number of layers.

Therefore a total weight of 10.2 kg m

-2

of reinforcement is required. The distribution of this would be selectedaccording to manufacturers' individual preferences, but one suitable configuration would be:

2 layers 300 g m-2

(one at each surface) = 0.6 kg m-2

16 layers 600 g m-2

= 9.6 kg m-2

Total = 10.2 kg m-2

Assuming a glass content of 30% for CSM, the wall thickness would be 2.2 mm per kg/m2

of glass, giving a total

wall thickness of 22.4 mm.

A more efficient structure is obtained using a combination ofCSMwith WR, in which case the laminate

construction is determined as follows:


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The design unit loading in the WRmust be reduced such that the strain does not exceed the design limit for CSM,

hence

per kg/m

2of glass

The design of the laminate can then be determined from

Therefore a suitable design would be as follows:

Detail Calculation Total

Reinforced gel coat - -

1500 g/m2

CSM 17.2 x 1.5 25.80

800 g/m2

WR

x5

22.6 x 0.8

x5 129.10

450 g/m

2

CSM17.2 x 0.45

800 g/m2

WR 22.6 x 0.8 18.08

300 g/m2

CSM 17.2 x 0.30 5.16

Resin rich layer with binding tissue - -

TOTAL 178.14

In this case, assuming a glass content of 30% for CSMwith 2.2 mm per kg/m2

of glass, and a glass content of

55% forCSMwith 0.95 mm per kg/m2

of glass, the vessel wall thickness would be 13.5 mm.

Dished End Design

If a torispherical end is desired for such a vessel, a typical geometry would be hi /Di= 0.25 and ri /Di= 0.15

(Note that this is slightly deeper than would be used for a typical metallic construction) .

At these values, the shape factorKs is approximately equal to 1.78. The membrane unit load for a domed end

subject to pressure is given by

For the current case, that is

Assuming a construction of CSM mat and woven rovings, similar to that for the vessel shell, gives a required

weight of reinforcement is given by

Therefore a suitable design would be as follows:

Detail Calculation Total

Reinforced gel coat - -

1200 g/m2

CSM 17.2 x 1.2 20.64

800 g/m2

WR x12 22.6 x 0.8 x12 309.84


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450 g/m2

CSM 17.2 x 0.45

800 g/m2

WR 22.6 x 0.8 18.08

300 g/m2

CSM 17.2 x 0.30 5.16

Resin rich layer with binding tissue - -

TOTAL 353.72

This gives an actual laminate thickness of 25.06, assuming a glass content of 30% forCSMwith 2.2 mm per

kg/m2

of glass, and a glass content of 55% forCSMwith 0.95 mm per kg/m2

of glass, as previously.

For a laminate of this thickness,

and the assumed value ofKs = 1.78 is reasonable. If it had been found that the value ofKs was not acceptable,

then the calculation would need to be repeated with a better estimate for the value of Ks until convergence was

achieved.

Reference: BS4994 - Specification for Vessels and Tanks in Reinforced Plastics, BSI 1973.

Keywords: BS4994, Design, Design strain, Part factors, Laminate, Code


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CDKB Pressure Vessel Design Case Study

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